When my kids were little we used to watch a show on PBS called "Musical Encounters." I believe it came from a West Coast television station, but wherever it was from, the show was remarkable. One show featured Josef Gingold and the 16-year-old Corey Cerovsek playing Wieniawski. Corey answered questions from the audience of young children about the dangers of playing in a tree house (what if a bird poops on your violin) and the paint on his violin ("actually, it's varnish" was a buzzword in our household for a while). Another show featured a pigtailed and freckled 9-year-old Leila Josefowicz storming through Boehm's Perpetual Motion, and another show featured two violin-playing brothers who were remarkable. When the audience asked them how they knew where the notes are on the violin, one brother's response was "you have to practice."
I often think of that simple statement when I am shifting around on the violin (or the viola today--it is an orchestra week, so I'm spending some quality time with my viola). Eventually we, by some mysterious alchemy and by a lot of practice, learn where the notes are up and down the strings the way we know where notes are in our own voices. It takes a long time, but once your body physically knows where a pitch is, the connection between hand and ear becomes automatic. It doesn't need to be interpreted by the conscious brain.